9 hundred baked bricks of^2 ⁄ 3 cubits each. I enlarged an animal yard. What is the
square side of the animal yard? You go 0 ; 40 steps for each brick. You take 30
each of 15 00. You go 30 steps of 0 ; 40 : 20. The square side of the animal yard
is 20 cubits.The solution is simply to find the number of bricks that would make up the edge
of the square area, by finding the square root of the total number (happily a square
integer), then to multiply by the length of each brick. Although the problem itself
is reminiscent of OB mathematics, the technical terminology and method of solution
are both radically different.
Three tablets from Shamash-iddin’s house bear metrological tables and reciprocal
tables. Two contain various tables relating length and both systems of area measure
to each other and to the sexagesimal system, and to various time-keeping schemes.
One begins with a list of numerical writings for the major gods. The third tablet is
a common first-millennium table of many-place reciprocal pairs from 1 to 4. It appears
to have been calculated, at least in part, not simply copied from another exemplar,
as witnessed by two rough tablets with nine calculations of regular reciprocals taken
from near the beginning of the table. The original number is multiplied repeatedly
by simple factors of 60 until it is reduced to 1 ; then 1 is multiplied up again by
those same simple factors in reverse: once more, a favourite OB school problem is
solved using a new method (Friberg 1999 ).
Mathematics for kalûsThe latest dateable mathematical cuneiform tablets were written by members of the
Sîn-leqi-unninni family in Seleucid Uruk. The Sîn-leqi-unninnis are the best known
of all the scribal families of Late Babylonian Uruk, partly because their eponymous
ancestor was considered to be the author of the famous Epic of Gilgamesh, and partly
because they have left a vast amount of documentary evidence (Beaulieu 2000 ). While
most of their tablets come from uncontrolled excavation (Thureau-Dangin 1922 ),
several were found in the Resh temple of Anu in the city centre (van Dijk and Mayer
1980 ). Anu-belshunu and his son Anu-aba-uter, who worked there as kalûs, or
lamentation priests, wrote and owned a large number of mathematical astronomical
tablets, mostly ephemeredes, or tables of predictions. Unlike other scribal families,
they put their name to very few copies of the standard series of omens or medical
compilations, but concentrated instead on the kalûtu, the standard series of incantations
and rituals associated with their profession as lamentation priests working for Anu’s
temple Resh in Uruk city centre. Their scholarly tablets almost all reflect their
professional concerns: the mathematical prediction of ominous celestial events, and
the correct performance of ritual reactions to them (Pearce and Doty 2000 ).
Anu-belshunu made a copy of the ‘Esangila tablet’, for a member of another scribal
family, in the 220 s BCE. This text, known also from the vicinity of Babylon, uses
the measurements of the great courts and the ziggurat Etemenanki near Marduk’s
temple Esangila as a pretext for some simple metrological exercises in seed and reeds,
the different kinds of area measure (AO 6555 : George 1993 : 109 – 19 , 414 – 34 ).
Anu-aba-uter’s compilation of mathematical problems, which must have been
written in the 180 s BCE, is the latest datable mathematical cuneiform tablet known.
— Mathematics, metrology and professional numeracy —